Solução de equações de balanço populacional usando a técnica da transformada de Laplace e filtro de partículas

Abstract

The evolution of particle size distribution in many fields of applied science, such as crystallization, aerosols, colloids, and polymer processing, can be obtained by solving population balance equation (PBE). The Laplace transform technique with numerical inversion was used to solve an integro-partial-differential equation related to the mathematical modeling of the physical problem to study convective processes with birth and death rates of particles or aerosols. Such model is governed by the population balance equation (PBE), in which is taken into account the nucleation, growth and coagulation processes. A Bayesian method was employed to solve the hyperbolic and non-linear inverse problem and estimate the size distribution density function, thus predicting the dynamic behavior of the physical system. Specifically the particle filter with sampling Importance Resampling (SIR) has been applied as a method of solving the problem. From these solutions, numerical results were obtained and compared with those in the literature for particulate systems permitting a critical evaluation of the present solution methodology.